20.500.12556/DKUM-59108 Uvod v linearni strig An introduction to transvections Pregledno in izčrpno je predstavljen pojem linearnega striga in osrednja vloga te linearne preslikave na področju linearne algebre. Njegova vpeljava je izvedena postopno in zložno z eksplicitno opredelitvijo s predpisom učinkovanja ter geometrijsko ponazoritvijo, najprej na realnem dvorazsežnem in trirazsežnem vektorskem prostoru geometrijskih vektorjev in nato na poljubnem končnorazsežnem vektorskem prostoru nad poljubnim poljem. Predstavljene so raznovrstne med seboj enakovredne opredelitve pojma linearni strig. Posebna pozornost je posvečena poimenovanju linearnega striga. Navedene in dokazane so temeljne lastnosti linearnih strigov na končnorazsežnem vektorskem prostoru, med katerimi je posebnega pomena ta, da linearni strigi netrivialnega končnorazsežnega vektorskega prostora razsežnosti najmanj dva generirajo njegovo posebno linearno grupo. Utemeljen je elementarni značaj linearnega striga v linearni algebri. Za vsako enoto z obsežnega seznama učbenikov s področja uvoda v linearno algebro ter teorije grup je navedeno, ali je linearni strig sploh omenjen ter v pozitivnih primerih njegova opredelitev in obravnavani rezultati. The notion of transvection and its central role in linear algebra is presented transparently and comprehensively. Its introduction is performed gradually and gently with the definition through the rule of action and its geometric illustration, first on the real two- and three-dimensional vector spaces of geometric vectors, then on an arbitrary finite dimensional vector space over an arbitrary field. Miscellaneous equivalent definitions of the term transvection are given. Special attention is devoted to the denomination of transvections. Basic properties of transvections on finite dimension vector spaces are stated and their proof given, and among them of special meaning that transvections of a finite dimensional vector space of dimension at least two generate its special linear group. The elementary character of transvections in linear algebra is substantiated. An extensive list of linear algebra and group theory textbooks is examined and a report specifies for each item whether transvections are mentioned, and in positive cases the underlying definition and results. linearni strig vektorski prostor endomorfizem linearen funkcional transvection vector space endomorphism linear form shear mapping true true false [G. Lah] Slovenski jezik Angleški jezik Magistrsko delo 2016-05-04 13:50:34 2016-08-17 15:48:07 2022-06-19 03:06:51 2019-07-11 11:02:58 2016 0 Sežana 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.64(043.2) 22438152 URN:SI:UM:DK:NVYLTGX1 MAG_Lah_Gorazd_2016.pdf MAG_Lah_Gorazd_2016.pdf 1 2372D545614C655FDEB3353F38BE9C45 8320ff74b7f3ed8f139d49cf4a391a19f0e1ab89e1fa939fe6c2d5728f6b2db9 d0fe1bb5-7c0c-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=95805 Fakulteta za naravoslovje in matematiko 0 0 0